Multivariation and students’ multivariational reasoning

Covariation and covariational reasoning have become key themes in mathematics education research. In this paper, I build on the construct of covariation by considering cases where more than two variables relate to each other, in what I term “multivariation.” This paper provides two major contributions. The first is a conceptual analysis describing distinct theoretical multivariation structures: independent, dependent, and nested. The second is an empirical study that explored students’ mental actions in reasoning about multivariation. The results of this study showed that while students’ multivariational reasoning was, as expected, connected to covariational reasoning, there were many extensions and new mental actions used by the students. These included different types of recognizing, reducing multivariation into isolated covariations, switching variables and constants, different types of coordinating multiple simultaneous changes, and continuous multivariation consisting of imagining an entire system evolving.